An algorithm of variable structure based on three-stage explicit-implicit methods

An explicit three-stage Runge–Kutta type scheme and L-stable Rosenbrock method are derived, both schemes of order 3. A numerical formula of order 1 is developed on the base of the stages of the explicit third order method. The stability interval of the first order formula is extended up to 18. The integration algorithm of variable order and step is constructed on the base of these three schemes. For each integration step the most efficient numerical scheme is chosen using an inequality for stability control. Numerical results confirming efficiency of the algorithm are given.